Will AI always depend on models and thus approximations?
There's a neuroscience theory, known as predictive coding, which roughly states that the (human) brain is constantly generating and updating a model of the world.

The brain is constantly confronted with a wealth of sensory information that must be processed efficiently to facilitate appropriate reactions. One way of optimizing this processing effort is to predict incoming sensory information based on previous experience so that expected information is processed efficiently and resources can be allocated to novel or surprising information. Theoretical and computational studies led to the formulation of the predictive coding framework (Friston 2005, Hawkins and Blakeslee 2004, Mumford 1992, Rao and Ballard 1999). Predictive coding states that the brain continually generates models of the world based on context and information from memory to predict sensory input. In terms of brain processing, a predictive model is created in higher cortical areas and communicated through feedback connections to lower sensory areas. In contrast, feedforward connections process and project an error signal, i.e. the mismatch between the predicted information and the actual sensory input (Rao &amp; Ballard, 1999). The predictive model is constantly updated according to this error signal.

This theory should not be surprising or unintuitive, given that every person possesses a slightly different perspective (or model) of the world, which is based on her (or his) personal experiences. Of course, this is just a theory, which may not be the most precise one that describes our brain, but this theory is already being validated by a number of brain imaging studies investigating predictive feedback and the processing of prediction errors.
Therefore, artificial intelligence may not be the only entity that is based on or will be limited by a model of the world. To answer your question more directly, yes, the AI will always be limited by its model and environment (e.g. hardware), in a similar way that flatlanders are limited by their 2-dimensional nature and world, but this doesn't necessarily mean we will not be able to create useful (and even sophisticated or human-like) AI systems.